SOLUTION: Sketch the graph of f(x)=x^2-x-6 include all intercepts and the vertex

Question 58493: Sketch the graph of f(x)=x^2-x-6 include all intercepts and the vertex
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
f(x)=x^2-x-6
:

f(x) = y
:
y = x^2 - x - 6
:
Factors to:
(x-3)(x+2) = 0
x = +3 and x = -2; (the x intercepts)
:
y intercept when x = 0
y = 0^2 - 0 - 6
y = -6; (the y intercept)
:
The vertex is the value of x when the parabola is at minimum
Can be found using the vertex equation: x = -b/(2a)
:
In the form, ax^2 + bx + c, your equation: a = =1, b = -1, c = -6 (not used)
x = -b/(2a)
x = -(-1)/(2*1)
x = +1/2
x = .5 is the vertex, (as you can see by the graph)
:
They did not ask what the minimum value (y) is but if you wanted to find it,
Substitute .5 for x in the original equation:
y = .5^2 - .5 - 6
y = .25 - .5 - 6
y = -6.25 is the minimum and occurs at the vertex, x = .5 (see graph)

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